Prof. Salvador Barberà(Universitat Autònoma de Barcelona, Catalonia)Some new domain restrictions in social choice, and their consequences

Authors: Salvador Barberà, Dolors Berga, Bernardo Moreno

Abstract:
Restricting the domains of definition of social choice functions is a classical method to test the robustness of impossibility results and to find conditions under which attractive methods to reach collective decisions can be identified, satisfying different sets of desirable properties. We survey a number of domains that we have recently explored, and exhibit the possibility results that emerge for functions defined on each one of them. In particular, we have identified conditions under which the social preference relations derived by different supermajority voting systems would satisfy quasitransitivity, others where individual and group strategy-proofness would become equivalent, and still others where the strategy-proofness of social choice functions is guaranteed as soon as they satisfy very simple monotonicity and invariance requirements.
Our main message is that every specific social choice problem deserves a careful analysis of the domains on which we need to define the method to be used, since this may open the door to attractive possibility results.

Prof. Endre Pap( Academy of Sciences and Arts of Vojvodina, Serbia)Theory and applications of non-additive measures and corresponding integrals

Abstract: In multi-expert decision making problems, the use of interval-valued fuzzy sets poses the problem of the non-existence of a natural total
order to rank the alternatives. We consider here the class of admissible
orders, which are total orders between intervals defined in terms of two
aggregation functions. We make use of such orders to define
interval-valued OWAs and Choquet integrals in such a way that, if the
intervals degenerate into single points, we recover the classical
concept of such aggregations. We then show that the choice of the linear
order determines the solution of the given mutiexpert decision making
problem, in a such a way that we can pick any solution up beforehand
just by selecting the appropriate linear order. For this reason, we end
proposing two algorithms such that second one allows us, by means of the
Shapley value, to pick up the best alternative from a set of winning
alternatives provided by the first algorithm.